Beautiful and surprising patterns abound in \(\mathcal {P}\)  much as in \(\mathbb {N}\) ; and in the values of these partition statistics, one observes striking arithmetic properties which often require subtle methods to prove. Partitions have been connected to algebra since the work of Cauchy [1]}; in recent years, ideas from algebra are used more and more to study partitions themselves as algebraic and set-theoretic objects on equal footing with numbers. This shift can perhaps be traced to G. E. Andrews' far-reaching theory of partition ideals developed in the 1960s and 70s based on ideas from lattice theory ([2]}, Ch. 8), and to a seminal 1977 paper of Alladi and Erd [3]}, which employs a natural bijection between partitions into prime parts and prime factorizations of integers, to prove analytic properties of arithmetic functions.
